Question: Find the slope and y-intercept of the line that is ${\text{parallel}}$ to $\enspace {y = -x + 5}\enspace$ and passes through the point ${(5, 2)}$. {1} {2} {3} {4} {5} {6} {7} {8} {9} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {1} {2} {3} {4} {5} {6} {7} {8} {9} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9}
Parallel lines have the same slope. The slope of the blue line is ${-1}$ , so the equation of our parallel line will be of the form $\enspace {y = -x + b}\enspace$ We can plug our point, $(5, 2)$ , into this equation to solve for ${b}$ , the y-intercept. $2 = {-}(5) + {b}$ $2 = -5 + {b}$ $2 + 5 = {b} = 7$ The equation of the parallel line is $\enspace {y = -x + 7}\enspace$. ${m = -1, \enspace b = 7}$